A033690 Theta series of A2[hole]^4.

1, 4, 14, 28, 57, 84, 148, 196, 312, 364, 546, 624, 910, 988, 1352, 1456, 1974, 2072, 2710, 2800, 3705, 3724, 4816, 4788, 6188, 6076, 7658, 7644, 9620, 9352, 11536, 11284, 14183, 13468, 16542, 15996, 19864, 18928, 22820, 21904, 26880, 25284

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Examples

			q^4 + 4*q^7 + 14*q^10 + 28*q^13 + 57*q^16 + 84*q^19 + 148*q^22 + ...
		

References

• J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 111, Eq (63)^4.

Crossrefs

Cf. A033685.

Programs

Mathematica

s = (QPochhammer[q^3]^3/QPochhammer[q])^4 + O[q]^45; CoefficientList[s, q] (* Jean-François Alcover, Nov 04 2015 *)

PARI

{a(n) = local(A); if(n<0, 0, A = x*O(x^n); polcoeff( (eta(x^3 +A)^3 / eta(x +A) )^4, n))} /* Michael Somos, Aug 22 2007 */

Formula

a(n) = A033685^4.

Expansion of q^(-4/3) * (eta(q^3)^3 / eta(q))^4 in powers of q. - Michael Somos, Aug 22 2007

Expansion of c(q)^4 / (81 * q^(4/3)) in powers of q where c() is a cubic AGM function. - Michael Somos, Aug 22 2007

Euler transform of period 3 sequence [ 4, 4, -8, ...]. - Michael Somos, Aug 22 2007

A092342(n) = A000731(n) + 81*a(n-1). - Michael Somos, Aug 22 2007